Microbeams are key elements in most of the micro-electromechanical systems (MEMS). Electromechanical instability of microbeams in turn plays an important role in their applications. *e shape and mechanical properties of microbeams dictate their functional characteristics. Focusing on their instability-based working mechanism, one can appreciate that viscoelasticity of MEMS materials cannot be neglected. Consequently, the analysis of instability in viscoelastic curved microbeams is an essential demand. In this research, assuming a clamped-clamped initially curved microbeam, the effects of viscoelastic behavior on the snap-through and pull-in instabilities are investigated. *e standard inelastic linear solid model is used for the simulation of viscoelastic behavior. Integrodifferential governing equation of the curved viscoelastic microbeam is obtained by assuming modified couple stress theory and using Hamilton’s principle. By applying the Galerkin method, the obtained governing equation is discretized, converted to a nonlinear differential equation, and solved by MATLAB software. *rough a quasi-static analysis, the voltage and location of snap-through and pull-in instabilities are identified. *e effects of different viscoelastic parameters including the creep moduli and relaxation coefficient upon the snap-through and pull-in instabilities are investigated. *e effects of different short- and long-term creeping characteristics of viscoelastic microbeam are studied and discussed in detail.

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